5 Calculation of the required capital contribution rate for the New Zealand Superannuation Fund
The New Zealand Superannuation Act 2001 requires the Treasury annually to determine the capital contribution required to be made from the Crown to the Fund for the next financial year. This must be set so that, if that same proportion of forecast GDP were to be made to the Fund each year for the succeeding forty years, the Fund balance plus accumulated returns would be just sufficient to meet the expected net cost of entitlement payments over those forty years. This can be expressed as:[15]
(8)
where:
B0 = Fund balance at the beginning of year 1.
H = time horizon for the calculation. This is set at forty years.
rt = rate of return on the Fund in year t.
k1 = total contribution rate for year 1 as a proportion of GDP.
Gt = GDP for year t.
Pt = forecast entitlement payments in year t.
And the required capital contribution for the next period (in $) is:
(9)
Solving the above expectation equation for the total contribution rate (k1) gives:[16]
(10)
The summation terms in both the numerator and the denominator in this equation are analogous to present value calculations and the appropriate discount rate is E[r], which is the expected annual arithmetic return on the investment portfolio of the Fund.[17] If the expected geometric return were to be used in this calculation, the required contribution rate would be misstated.
Notes
- [15]This is a simplified version being used here to explain the principles at issue. A more detailed version is used for the actual calculation, taking into account such things as the fortnightly payment structure (McCulloch and Frances 2001).
- [16]This solution is explained in detail in McCulloch and Frances (2001).
- [17]Note that the summation terms are not actually calculations of the present values of the cashflow streams, Pt and Gt. That would require the use of discount rates that reflected the risk inherent in those cashflow streams, and not the expected return on the investment portfolio.
